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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The solution of $y^{2}+^{2n}=x^{3}$
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by Stanley Rabinowitz PDF
Proc. Amer. Math. Soc. 62 (1977), 1-6 Request permission

Abstract:

All solutions to the diophantine equation \begin{equation}\tag {$\ast $}{y^2} + \gamma {2^n} = {x^3};\quad \gamma = \pm 1,\end{equation} are found.
References
  • A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
  • Robert D. Carmichael, The theory of numbers and Diophantine analysis, Dover Publications, Inc., New York, 1959. MR 0105381
  • B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Translations of Mathematical Monographs, Vol. 10, American Mathematical Society, Providence, R.I., 1964. MR 0160744
  • L. Euler, Comm. Acad. Petrop. 10 (1738), 145; Comm. Arith. Coll. I, 33-34; Opera Omnia, (1), II, 56-58.
  • Ove Hemer, On the solvability of the Diophantine equation $ax^2+by^2+cz^2=0$ in imaginary Euclidean quadratic fields, Ark. Mat. 2 (1952), 57โ€“82. MR 49917, DOI 10.1007/BF02591382
  • W. J. Le Veque, Topics in number theory, Vol. II, Addison-Wesley, Reading, Mass., 1961.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 62 (1977), 1-6
  • MSC: Primary 10B25
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0424678-9
  • MathSciNet review: 0424678